Unfortunately, with open (or even just somehow permeable) borders, any noticeable delta in lifestyle would just be gobbled up by slow population displacement from shamelessly breeding places. There at no panacea solutions. I envy those born a decade earlier and pity those born a decade later.
In the current system, however, a country who keeps their population low will have small allowances; It clearly incentives overpopulating its land. This inverse-incentive effect may provoke countries into doing nothing against evergrowing population, keeping cost of life too affordable, and thus, ensuring that the next generation will be overpopulated, and thus, extenuating the land.